Finite Group DatabasebetaFinite Group DatabasebetaOrder 16832.
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16862363 | C2 | semidirect |
| 2. C2×C8×D263 | C2 | semidirect |
| 3. #22554446 | C2 | semidirect |
| 5. #22554401 | C2 | semidirect |
| 6. #22554392 | C2 | semidirect |
| 7. #103×C263 | C2 | semidirect |
| 30. C263⋊C8 | D4 | semidirect |
| 43. C2×D263 | SD16 | semidirect |
| 55. C263 | #465 | semidirect |
| 62. #103 | D263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862363 | 2 |
| C2×C8×D263 | 2 |
| #22554446 | 2 |
| #22554445 | 2 |
| #22554401 | 2 |
| #22554392 | 2 |
| #103×C263 | 2 |
| #465 | 263 |